A113470 - OEIS

%I #15 Jan 03 2020 05:31:27

%S 1,2,3,3,5,7,5,11,17,23,5,11,17,23,29,7,37,67,97,127,157,35,65,95,125,

%T 155,185,215,635,707,779,851,923,995,1067,1139,635,707,779,851,923,

%U 995,1067,1139,1211,199,409,619,829,1039,1249,1459,1669,1879,2089,3841,3973

%N Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same number of divisors.

%C In this sequence "smallest" means that the last term of the arithmetic progression is minimized and if there is still a choice then we minimize the common difference of the arithmetic progression.

%H OEIS wiki, <a href="https://oeis.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.

%F T(n,k) = A090547(n) + (k-1)*A090549(n). - _R. J. Mathar_, May 11 2007

%e From _M. F. Hasler_, Jan 02 2020: (Start)

%e The triangle starts

%e     n | row n

%e    ---+------------

%e     1 |    1,

%e     2 |    2,    3,

%e     3 |    3,    5,    7,

%e     4 |    5,   11,   17,   23,

%e     5 |    5,   11,   17,   23,   29,

%e     6 |    7,   37,   67,   97,  127,  157,

%e     7 |   35,   65,   95,  125,  155,  185,  215,

%e     8 |  635,  707,  779,  851,  923,  995, 1067, 1139,

%e     9 |  635,  707,  779,  851,  923,  995, 1067, 1139, 1211,

%e    10 |  199,  409,  619,  829, 1039, 1249, 1459, 1669, 1879, 2089,

%e    11 | 3841, 3973,  ...

%e Most rows so far consist of primes with 2 divisors, rows 7, 8, 9 and 11 have squarefree semiprimes with 4 divisors.

%e Row 10 is A033168; also row 10 of A086786, A133276 and A133277. (End)

%Y Cf. A086786, A090547, A090548, A090549.

%K nonn,tabl

%O 1,2

%A _David Wasserman_, Jan 08 2006